In this paper, three forms of orthogonal frequency division multiplexing (OFDM) designed for intensity modulated/direct detection (IM/DD) optical systems are compared. These are asymmetrically clipped optical OFDM (ACO-OFDM), DC biased optical OFDM (DCO-OFDM) and asymmetrically clipped DC biased optical OFDM (ADO-OFDM). ADO-OFDM is a new technique that combines aspects of ACO-OFDM and DCO-OFDM by simultaneously transmitting ACO-OFDM on the odd subcarriers and DCO-OFDM on the even subcarriers. The odd subcarriers are demodulated as in a conventional ACO-OFDM receiver and the even subcarriers are demodulated using a form of interference cancellation. ADO-OFDM is shown to be more optically power efficient than conventional ACO-OFDM and DCO-OFDM, for some bit rate/normalized bandwidths. It is also shown that by varying the proportion of optical power on the ACO-OFDM component, the DC bias level of DCO-OFDM and the constellations sent on the odd and even subcarriers, the optical power efficiency of ADO-OFDM can be changed.